Proving a limit does not exist via delta epsilon

The limit of 1/(x^2-4) does not exist as x approaches 2- this makes sense since for any delta there are value of x that are arbitrarily 'close' to 2, thus making 1/(x^2-4) infinitely large, so no possible L will make 1/(x^2-4)-L<epsilon for a given epsilon. However, I don't know how to turn this into a formal statement. Any tips?

The limit of 1/(x^2-4) does not exist as x approaches 2- this makes sense since for any delta there are value of x that are arbitrarily 'close' to 2, thus making 1/(x^2-4) infinitely large, so no possible L will make 1/(x^2-4)-L<epsilon for a given epsilon. However, I don't know how to turn this into a formal statement. Any tips?